An amplitude-phase (Ermakov-Lewis) approach for the Jackiw-Pi model of bilayer graphene
K.V. Khmelnytskaya, H.C. Rosu
TL;DR
This paper develops a novel amplitude-phase approach for the Jackiw-Pi model of bilayer graphene, enabling numerical solutions and phase calculations that could inform future experiments.
Contribution
It introduces an Ermakov-Lewis method to analyze the Jackiw-Pi model, including a generalization of the nonlinear Darboux transformation.
Findings
Numerical solutions for the model in powers of bias potential V
Calculation of Lewis-Riesenfeld phases relevant for experiments
Generalization of nonlinear Darboux transformation
Abstract
In the context of bilayer graphene we use the simple gauge model of Jackiw and Pi to construct its numerical solutions in powers of the bias potential V according to a general scheme due to Kravchenko. Next, using this numerical solutions, we develop the Ermakov-Lewis approach for the same model. This leads us to numerical calculations of the Lewis-Riesenfeld phases that could be of forthcoming experimental interest for bilayer graphene. We also present a generalization of the Ioffe-Korsch nonlinear Darboux transformation
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